Iven AB as shown at the right. Find the coordinates of partition point P that divides the segment into a 3:1 ratio. (don't forget to convert the ratio into a fraction) *

Given AB  as shown at the right. Find the coordinates of partition point P that divides directed segment AB into a 3:1 ratio.

( 0 , - 1 )

Step-by-step explanation:

Let the initial point be A (-8, -5)

And the end point be B (8, 3)

( X2 - X1),(Y2 - Y1) = ( 8- -8),(3- -5)

That is (8+8),(3+5) = 16 , 8

The partitions of the segment AB is into a ratio 3 to 1

(16 × 3, 8 × 3) = 48 , 24

Divide both by 6 to get the Lowest term.

8 , 4

Add the two coordinate to the coordinate at point A

The segiment coordinate point from the initial point will be

(-8+8 , -5+4 ) = ( 0 , - 1 )

Please find the attached file for the figure.

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

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